A357138 Minimal run-length of the n-th composition in standard order; a(0) = 0.

0, 1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,4

Comments

A composition of n is a finite sequence of positive integers summing to n. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. This gives a bijective correspondence between nonnegative integers and integer compositions.

Links

Table of n, a(n) for n=0..86.

Gus Wiseman, Statistics, classes, and transformations of standard compositions

Example

Composition 92 in standard order is (2,1,1,3), so a(92) = 1.

Mathematica

stc[n_]:=Differences[Prepend[Join @@ Position[Reverse[IntegerDigits[n, 2]], 1], 0]]//Reverse;
Table[If[n==0, 0, Min[Length/@Split[stc[n]]]], {n, 0, 100}]

Crossrefs

See link for more sequences related to standard compositions.

The version for Heinz numbers of partitions is A051904, for parts A055396.

For parts instead of run-length we have A333768, maximal A333766.

The opposite (maximal) version is A357137.

For first instead of minimal we have A357180, last A357181.

Cf. A000120, A001511, A003754, A029931, A051903, A056239, A061395, A070939, A297173, A356844, A357136.

Sequence in context: A337066 A324247 A138904 * A357180 A196660 A342323

Adjacent sequences: A357135 A357136 A357137 * A357139 A357140 A357141

Keyword

nonn

Author

Gus Wiseman, Sep 18 2022

Status

approved